A genetically modified mouse is provided, wherein the mouse expresses an immunoglobulin light chain repertoire characterized by a limited number of light chain variable domains. Mice are provided that express just one or a few immunoglobulin light chain variable domains from a limited repertoire in their germline. Methods for making bispecific antibodies having universal light chains using mice as described herein, including human light chain variable regions, are provided. Methods for making human variable regions suitable for use in multispecific binding proteins, e.g., bispecific antibodies, and host cells are provided. Bispecific antibodies capable of binding first and second antigens are provided, wherein the first and second antigens are separate epitopes of a single protein or separate epitopes on two different proteins are provided.